CN117933316B - Groundwater level probability forecasting method based on interpretable Bayesian convolution network - Google Patents

Abstract

The invention discloses a ground water level probability forecasting method based on an interpretable Bayesian convolution network, which utilizes a leading edge time sequence forecasting model and a Bayesian method to realize ground water level reliable probability forecasting, and utilizes an interpretation algorithm to identify and quantify the contribution degree of each input characteristic to ground water level forecasting results. The invention can convert the one-dimensional time sequence into the two-dimensional space based on the periodic characteristics of the one-dimensional time sequence, and then extract the periodic characteristics of the sequence through the convolution network, thereby realizing the reliable forecast of the groundwater level. The invention combines the Monte Carlo discarding Bayesian method and the SHAP interpretability method, quantifies the uncertainty of the forecast result and the contribution degree of the input characteristics to the forecast result, and realizes the groundwater level probability and the interpretable forecast. Based on the ground water level monitoring data and the meteorological data, the ground water level monitoring system can realize reliable forecast of ground water level change in the future for one month, and provides decision support for ground water resource optimal allocation and ecological environment protection.

Description

A probabilistic groundwater level forecasting method based on interpretable Bayesian convolutional network

Technical Field

The present invention relates to the cross-technical field of hydrology and deep learning, and specifically to a groundwater level probability forecasting method based on an interpretable Bayesian convolutional network.

Background technique

Groundwater resources play an important role in agriculture, industry and drinking water supply. In addition, groundwater is also an important guarantee for maintaining ecological and environmental security. The groundwater level is a direct indicator of the availability of groundwater resources, and the change of groundwater level is also closely related to the stability of the ecosystem. Conducting groundwater level forecasting research and estimating the future trend of groundwater level changes can timely optimize the formulation of groundwater exploitation plans and ecological and environmental protection strategies, thereby achieving sustainable development of water resources and ecological and environmental protection.

There are many groundwater level forecasting technologies, which are mainly divided into two categories: traditional physics-driven numerical models and data-driven machine learning and deep learning methods. Among them, deep learning methods can overcome the limitation of large number of numerical model parameters and often have better forecasting performance than machine learning models with simpler structures. Therefore, they have been widely used in groundwater level forecasting in recent years. Despite this, deep learning forecasting methods still face some challenges, including the need to further improve the forecasting accuracy of the model, especially for groundwater level forecasting in the long forecast period, which is still not ideal; the black box property of deep learning models leads to poor interpretability of model forecasting results and unclear forecasting mechanism; in addition, most existing forecasting models are deterministic models that can only give a single forecast value and cannot quantify the uncertainty of the forecast results.

Summary of the invention

The purpose of the present invention is to provide a groundwater level probabilistic forecasting method based on an interpretable Bayesian convolutional network, which can achieve reliable forecasts of future groundwater level changes and quantify the uncertainty of the forecast through a Bayesian method. The SHAP interpretation algorithm adopted calculates the contribution of different input features to the results to solve the problem of unclear forecasting mechanism raised in the above background technology.

In order to solve the above technical problems, the present invention provides the following technical solution, a groundwater level probability forecasting method based on an interpretable Bayesian convolutional network, the steps of which include:

Determine the scope of the study area and obtain time series monitoring data of groundwater level monitoring wells in the study area;

Obtain meteorological factor data for groundwater level monitoring wells with the same geographical location within the time period covered by the corresponding time series monitoring data;

Divide the time period covered by the time series monitoring data into two time periods before and after a time node, the time period before the time node is called a training period, and the time period after the time node is called a test period;

Reorganizing the training period data and the test period data to construct an input-output sample training set and a test set;

Building an interpretable Bayesian convolutional network (XBCN), and training an interpretable Bayesian convolutional network (XBCN) groundwater level probability prediction model based on the input-output sample training set;

In the interpretable Bayesian convolutional network groundwater level probability prediction model, the Monte Carlo dropout method (MC-dropout) is used to randomly drop some neurons of the interpretable Bayesian convolutional network groundwater level probability prediction model N times according to probability during the prediction stage, and a forecast set consisting of N forecast results of the interpretable Bayesian convolutional network groundwater level probability prediction model is obtained;

Based on the input-output sample test set, the determination coefficient ( R ² ), root mean square error (RMSE) and Kling-Gupta efficiency coefficient (KGE) prediction accuracy of the trained interpretable Bayesian convolutional network groundwater level probability prediction model for each monitoring well in the next n time steps are calculated, and the prediction confidence interval is calculated based on the N forecast sets of the interpretable Bayesian convolutional network groundwater level probability prediction model;

The determination coefficient, the root mean square error and the Kling-Gupta efficiency coefficient are used as the judgment criteria to judge whether the interpretable Bayesian convolutional network groundwater level probability prediction model meets the prediction accuracy. If the prediction accuracy is not met, the interpretable Bayesian convolutional network training is continued to be used to optimize and adjust the interpretable Bayesian convolutional network groundwater level probability prediction model until the prediction accuracy is met;

Based on the explainable Bayesian convolutional network groundwater level probability forecasting model that meets the forecast accuracy, the SHAP (Shapely Additive exPlanations) interpretation algorithm is used to obtain the contribution of groundwater level, time and meteorological factors to the forecast groundwater level change;

According to the contribution of groundwater level, time and meteorological factors to the forecast of groundwater level change, the main influencing factors are determined, and the real-time monitoring data corresponding to the main influencing factors are input into the interpretable Bayesian convolutional network groundwater level probability forecasting model that meets the forecast accuracy for forecasting. The groundwater level, time and meteorological factors are called the main influencing factors.

According to the above technical solution, the meteorological factors include precipitation, evapotranspiration and temperature.

According to the above technical solution, the data in the training period is used to train the forecast model, and the data in the test period is used to evaluate the forecast accuracy of the model.

According to the above technical solution, the groundwater level data of m historical time steps, the meteorological factor data and the corresponding time data are used as input samples, and the groundwater level data of n future time steps are used as output samples to construct the input-output sample training set and test set.

According to the above technical solution, the meteorological factors, the groundwater level and the corresponding time data are input into the interpretable Bayesian convolutional network, and after being processed by a window normalization layer, an embedding layer and a fully connected layer in sequence, they are input into multiple stacked time modules TimesBlock to build the interpretable Bayesian convolutional network groundwater level probability forecasting model, wherein the interpretable Bayesian convolutional network groundwater level probability forecasting model can be referred to as the XBCN model;

The basic principle of TimesBlock is to utilize the multi-period superposition characteristics of time series, transform the time series from a one-dimensional vector to a two-dimensional space based on the fast Fourier transform, and then fully extract the potential features of the time series through a two-dimensional convolutional layer. Finally, the extracted features are converted back to one-dimensional space, and finally the groundwater level forecast value is obtained through a fully connected layer and an anti-normalization layer.

According to the above technical solution, based on the training set sample data, the constructed interpretable Bayesian convolutional network groundwater level probability prediction model is trained, and the mean square error is used as the loss function evaluation indicator to automatically train and optimize the interpretable Bayesian convolutional network groundwater level probability prediction model to obtain the optimal parameter combination.

In the test phase, the determination coefficient, root mean square error and Kling-Gupta efficiency coefficient are used as the judgment criteria, where the determination coefficient ( R ² ) is: ;

Root Mean Square Error (RMSE): ;

and Kling-Gupta efficiency factor (KGE): ;

In the formula, is the true value, /> is the average of the true values, /> is the forecast value, T is the number of observations, and the Kling-Gupta efficiency coefficient is 、/> and/> are the correlation coefficient, relative variability and deviation rate of the real sequence and the predicted sequence respectively, where/> represents the covariance of the forecast sequence and the true sequence,/> and/> are the standard deviations of the predicted and true series, respectively,/> and/> are the average values of the predicted series and the true series, respectively.

According to the above technical solution, when generating each forecast value, some neurons of the trained interpretable Bayesian convolutional network groundwater level probability forecast model are randomly discarded according to probability, and then a groundwater level forecast value is obtained based on the remaining neurons. This process is repeated N times to obtain a forecast set consisting of N forecast values.

According to the above technical solution, based on the forecast set, the average value of N forecast values is calculated. Standard Deviation/> , the upper and lower limits of the forecast confidence interval are obtained as/> (z is 1.64-2.58).

According to the above technical solution, the range of the forecast confidence interval is 90%-99%.

According to the above technical solution, the SHAP interpretation algorithm interprets the forecast results of the interpretable Bayesian convolutional network groundwater level probability forecast model as the sum of the contributions of meteorological factors, groundwater level and time, and the calculation formula is:

;

in, is the explanatory model, /> is the sample prediction value in the data set, /> is the average prediction value constant of all training samples, M is the sample /> The number of input features in / > is the sample prediction value/> Input features in /> The input characteristics include meteorological factor characteristics, groundwater level characteristics and time characteristics.

The attribution value of feature j can be calculated by the following formula:

;

in, is the set of all input features, /> is the number of input features, /> Indicates exclusion features/> All possible input feature sets after, /> It is the result of prediction using only the feature subset S. The input features include meteorological factor features, groundwater level features and time features. In this model, p=6.

Compared with the prior art, the beneficial effects achieved by the present invention are as follows: the present invention proposes a groundwater level probability prediction method based on an interpretable Bayesian convolutional network, which can realize reliable probability prediction of groundwater level in monitoring wells. The present invention uses a groundwater level probability prediction method based on an interpretable Bayesian convolutional network to improve the accuracy of groundwater level prediction, which helps decision makers to better plan and dispatch water resources and improve the efficiency of water resource utilization. The present invention integrates the Bayesian method into the convolutional network, quantifies the uncertainty of the prediction results in the form of confidence intervals, realizes the probability prediction of groundwater level, thereby improving the reliability of water resource management decisions and reducing decision risks. The SHAP interpretation algorithm is integrated into the convolutional network, and the interpretability of the model is enhanced by calculating the contribution of different input features to the results, thereby improving the reliability and credibility of the model. The real-time monitoring data of high-contribution input features can provide data support for future real-time prediction of groundwater levels. Compared with the prior art, the present invention improves the accuracy of groundwater level prediction, quantifies the uncertainty of the prediction results, and enhances the interpretability of the model.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings are used to provide a further understanding of the present invention and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention and do not constitute a limitation of the present invention. In the accompanying drawings:

FIG1 is a schematic diagram of the overall framework of a groundwater level probability forecasting method based on an interpretable Bayesian convolutional network according to the present embodiment;

Figure 2 (a) is a schematic diagram of the TimesBlock module structure;

Figure 2 (b) is a schematic diagram of the specific structure of the interpretable Bayesian convolutional network groundwater level probability prediction model;

Figure 3 is a graph showing the prediction accuracy evaluation of the interpretable Bayesian convolutional network groundwater level probability prediction model in the test set;

FIG4 is a graph showing the prediction results of a well in the test set of the interpretable Bayesian convolutional network groundwater level probability prediction model;

FIG. 5 shows the contribution of various input features to groundwater level changes when forecasting different time steps in this embodiment.

Detailed ways

The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

Taking a semi-arid area in northwest China as an example, the groundwater level fluctuation trend of the monitoring wells in the area was predicted, and the uncertainty of the forecast results was quantified. The contribution of different input features to the forecast results was analyzed to illustrate a groundwater level probabilistic forecasting method based on an interpretable Bayesian convolutional network. The specific steps include:

Phase 1: Obtain the 5-day groundwater level monitoring data and geographical location of 45 groundwater monitoring wells in the region from 2010 to 2017. According to the geographical location of the monitoring wells and the time period covered by the monitoring data, extract the daily precipitation, daily evapotranspiration and daily average temperature data at the same location from 2010 to 2017, and convert the daily meteorological data into 5-day data of the same scale as the groundwater level series.

Phase 2: The groundwater level and meteorological factor data were divided into a training period and a testing period with July 2015 as the boundary. That is, the first 65% of the groundwater level and meteorological factor data sets of each monitoring well were taken as the training set, and the last 35% of the data sets were taken as the testing set.

Phase 3: Based on the training set and test set data obtained in Phase 2, the input-output sample set is constructed by reorganizing them respectively. The specific reorganization process is as follows: the groundwater level, precipitation, evapotranspiration, temperature, month and date of the historical 24 time steps are used as input data, and the groundwater level of the next 6 time steps is used as output data. The sliding window of the input sample is set to a length of 24 time steps (1 time step = 5 days), and the sliding window of the output sample is set to a length of 6 time steps. On the time series data, the sliding window of the input sample is moved by a length of 1 time step from the beginning to the moment before the last output sample length in chronological order to obtain the input sample of each well. On the time series data, the sliding window of the output sample is moved by a length of 1 time step from the moment after the first input sample length to the end moment in chronological order to obtain the output sample of each groundwater monitoring well.

Phase 4: The input samples of the training set are put into the interpretable Bayesian convolutional network groundwater level probability prediction model (trained in ), and the output results are obtained. The mean square error is used as the loss function evaluation index, and the interpretable Bayesian convolutional network groundwater level probability prediction model is automatically trained and optimized to obtain the optimal parameter combination. The Monte Carlo dropout (MC-dropout) method is used in the interpretable Bayesian convolutional network groundwater level probability prediction model. When generating each forecast value, some neurons of the trained XBCN model are randomly discarded according to probability, and then a groundwater level forecast value is obtained based on the remaining neurons. The process is repeated N times to obtain a forecast set consisting of N forecast values. The model training uses a dropout rate of 0.05, a sample batch size of 16, and a learning rate of 0.001. Figure 2 (a) shows a schematic diagram of the TimesBlock module structure, where softmax represents a normalized exponential function, and the Inception module belongs to the prior art and is not explained in detail here.

Stage 5: Put the test set input samples into the interpretable Bayesian convolutional network groundwater level probability forecasting model to obtain the output groundwater level forecast results for the next 1-6 time steps. The relevant indicators such as determination coefficient ( ^R2 ), root mean square error (RMSE) and Kling-Gupta efficiency coefficient (KGE) are used to evaluate the forecast accuracy. If the forecast accuracy does not meet the requirements, return to stage 4 to optimize and adjust the interpretable Bayesian convolutional network groundwater level probability forecasting model parameters until the forecast accuracy is met.

Stage 6: Obtain an interpretable Bayesian convolutional network groundwater level probability forecasting model that meets the forecast accuracy. The model accuracy index evaluation results are shown in Figure 3. Figure 3 (a)-(f) are the results of forecasting the next 1-6 time steps respectively. The forecast accuracy of 1-6 time steps is averaged, and the average root mean square error (RMSE) of 45 wells in the region is 0.21, the average determination coefficient (R2) is 0.73, and the average Kling-Gupta efficiency coefficient (KGE) is 0.85. Based on the N forecast result sets obtained in Stage 4, the average value of the N forecast values is calculated. and standard deviation/> , the upper and lower limits of the 95% confidence interval of the forecast are/> (z is 1.96). The first/> The prediction curve of the groundwater monitoring well is shown in Figure 4. It can be seen from Figure 4 that the prediction curve of the interpretable Bayesian convolutional network groundwater level probability prediction model can fit the observed value well.

Stage 7: Based on the interpretable Bayesian convolutional network groundwater level probability forecasting model that meets the forecast accuracy obtained in stage 5, the SHAP algorithm is used to calculate the contribution of each input feature of all samples to the output (SHAP value). The absolute value of the SHAP values of all samples is averaged and normalized to obtain the SHAP result diagram in Figure 5. The ordinate in the figure is the model input feature, which is date, month, precipitation, evapotranspiration, temperature and historical groundwater level from top to bottom. The abscissa is the normalized result after the average absolute value of the SHAP value of each feature. (a)-(f) in Figure 5 represent the SHAP results of the forecast of 1-6 time steps in the future. It can be seen from Figure 5 that the historical groundwater level is the most important input feature. As the forecast time step increases, the influence of the historical groundwater level is gradually weakened, and the influence of other meteorological factors and monthly input features gradually increases. This may be because the response of the groundwater level to precipitation and evapotranspiration has a certain lag effect. In addition, the month is also a relatively important input variable, which can reduce the impact of abnormal values of meteorological input data on the results to a certain extent.

Phase 8: Based on the contribution results of each input feature quantified in Phase 7, focus on collecting real-time monitoring data of groundwater levels and input them into the interpretable Bayesian convolutional network groundwater level probability forecasting model that meets the forecast accuracy obtained in Phase 5. This can achieve real-time and reliable forecasts of future groundwater levels, and provide technical support for future rational planning of water resources and real-time early warning of ecological water levels.

It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device.

Finally, it should be noted that the above is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art can still modify the technical solutions described in the aforementioned embodiments or replace some of the technical features therein by equivalents. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims (10)

1. A method for groundwater level probability forecasting based on an interpretable Bayesian convolutional network, characterized in that the steps include: Determine the scope of the study area and obtain time series monitoring data of groundwater level monitoring wells in the study area; Obtain meteorological factor data for groundwater level monitoring wells with the same geographical location within the time period covered by the corresponding time series monitoring data; Divide the time period covered by the time series monitoring data into two time periods before and after a time node, the time period before the time node is called a training period, and the time period after the time node is called a test period; Reorganizing the training period data and the test period data to construct an input-output sample training set and a test set; Building an interpretable Bayesian convolutional network, and training an interpretable Bayesian convolutional network groundwater level probability prediction model based on the input-output sample training set; In the interpretable Bayesian convolutional network groundwater level probability prediction model, the Monte Carlo discarding method is used to randomly discard some neurons of the interpretable Bayesian convolutional network groundwater level probability prediction model N times according to probability during the forecasting stage, and a forecast set consisting of N forecast results of the interpretable Bayesian convolutional network groundwater level probability prediction model is obtained; Based on the input-output sample test set, the determination coefficient, root mean square error and Kling-Gupta efficiency coefficient prediction accuracy of the trained interpretable Bayesian convolutional network groundwater level probability prediction model for each monitoring well in the next n time steps are calculated, and the prediction confidence interval is calculated based on the N forecast sets of the interpretable Bayesian convolutional network groundwater level probability prediction model; The determination coefficient, the root mean square error and the Kling-Gupta efficiency coefficient are used as the judgment criteria to judge whether the interpretable Bayesian convolutional network groundwater level probability prediction model meets the prediction accuracy. If the prediction accuracy is not met, the interpretable Bayesian convolutional network training is continued to be used to optimize and adjust the interpretable Bayesian convolutional network groundwater level probability prediction model until the prediction accuracy is met; Based on the interpretable Bayesian convolutional network groundwater level probability forecasting model that meets the forecast accuracy, the SHAP interpretation algorithm is used to obtain the contribution of groundwater level, time and meteorological factors to the forecast of groundwater level changes; According to the contribution of groundwater level, time and meteorological factors to the predicted groundwater level changes, the main influencing factors are determined, and the real-time monitoring data corresponding to the main influencing factors are input into the interpretable Bayesian convolutional network groundwater level probability forecasting model that meets the forecast accuracy for forecasting. 2. According to the method for groundwater level probability forecasting based on an interpretable Bayesian convolutional network according to claim 1, it is characterized in that the meteorological factors include precipitation, evapotranspiration and temperature. 3. According to the method for groundwater level probability forecasting based on an interpretable Bayesian convolutional network described in claim 1, it is characterized in that the training period data is used to train the forecasting model, and the data in the test period is used to evaluate the forecasting accuracy of the model. 4. According to the method for groundwater level probability forecasting based on an interpretable Bayesian convolutional network described in claim 1, it is characterized in that the groundwater level data, meteorological factor data and corresponding time data of historical m time steps are used as input samples, and the groundwater level data of future n time steps are used as output samples to construct the input-output sample training set and test set. 5. According to the method for groundwater level probability forecasting based on an interpretable Bayesian convolutional network described in claim 1, it is characterized in that meteorological factor data, groundwater level data and corresponding time data are input into the interpretable Bayesian convolutional network, and are processed in sequence by a window normalization layer, an embedding layer and a fully connected layer, and then input into multiple stacked time modules TimesBlock to build the interpretable Bayesian convolutional network groundwater level probability forecasting model. 6. According to the method for groundwater level probability prediction based on an interpretable Bayesian convolutional network according to claim 1, it is characterized in that the constructed interpretable Bayesian convolutional network groundwater level probability prediction model is trained based on the training set sample data, and the mean square error is used as the loss function evaluation index to automatically train and optimize the interpretable Bayesian convolutional network groundwater level probability prediction model to obtain the optimal parameter combination. 7. According to claim 1, a groundwater level probability forecasting method based on an interpretable Bayesian convolutional network is characterized in that when generating each forecast value, some neurons of the trained interpretable Bayesian convolutional network groundwater level probability forecasting model are randomly discarded according to probability, and then a groundwater level forecast value is obtained based on the remaining neurons, and a forecast set consisting of N groundwater level forecast values is obtained by looping N times. 8. A method for predicting groundwater level probability based on an interpretable Bayesian convolutional network according to claim 1, characterized in that, based on the forecast set, an average value of N forecast values is calculated Standard Deviation/> , the upper and lower limits of the forecast confidence interval are obtained as/> . 9. The method for groundwater level probability prediction based on an interpretable Bayesian convolutional network according to claim 1 is characterized in that the prediction confidence interval ranges from 90% to 99%. 10. According to claim 1, a groundwater level probability forecasting method based on an interpretable Bayesian convolutional network is characterized in that the SHAP interpretation algorithm interprets the forecast result of the interpretable Bayesian convolutional network groundwater level probability forecasting model as the sum of the contribution of meteorological factors, groundwater level and time, and the calculation formula is: ; in, is the explanatory model,/> is the sample prediction value in the data set, /> is the average prediction value constant of all training samples, M is the sample /> The number of input features in / > is the sample prediction value/> Input features in/> The input characteristics include meteorological factor characteristics, groundwater level characteristics and time characteristics.